Wannier spread functionals in CP2K

[Pouya Partovi]

Hi everyone,

It appears (at least to me) that the localization of the Wannier orbitals 
in CP2K should be based on the work of Berghold et al., Phys. Rev. B 61, 10040 
(2000). However, in the output, after the localization phase, the code 
prints:

"Spread Functional sum_in -w_i ln(|z_in|^2) sum_in w_i(1-|z_in|^2)"

which are the spread functionals (Berghold et al., Eq. (13) and (14)) 
introduced by Resta (Phys. Rev. Lett. 82, 370 (1999)) and Silvestrelli 
(Phys. Rev. B 59, 9703 (1999)), respectively. The Berghold et al.'s 
introduced spread functional, however, reads

"sum_in w_i(1-|z_in|)" (Berghold et al., Eq. (12))

and has not been mentioned in the code, as far as I could get.

Could anyone please clarify which functional is exactly used in the code? 
Or perhaps I'm missing a point here?

Thanks in advance,
Pouya
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